Heat the oven to 350°.
For fresh tomatoes: Roast the tomatoes and chiles on a baking sheet 4 inches below a hot broiler, until they're darkly roasted. Turning to roast all sides. Cut off the tops of the chiles, shake out the seeds, remove most of the charred skin with your hands. Place roasted peppers and tomatoes in a food processor and blend to a smooth puree.
If using canned tomatoes: No need to roast canned tomatoes. Once the chiles are roasted, place canned tomatoes and roasted peppers into a food processor and blend to a smooth puree.
Cook The Onions: In a 4-5 quart Dutch oven, heat the oil (or lard, or bacon fat) over medium heat. Add the onion and cook, stirring regularly, until golden, about 5-7 minutes.
Make the Sauce: Raise the heat to medium-high, and stir in the tomato/pepper puree. Cook, stirring, until darker in color and thickened to the consistency of tomato paste, about 15 minutes.
Stir in the chicken broth, partially cover and simmer 15 minutes. Taste and season with salt, usually about 1/2 teaspoon. The sauce should be a slightly soupy consistency—not as thick as spaghetti sauce. If it is too thick, stir in a little additional broth. Stir the Mexican crema into the sauce. Keep warm over low heat.
Season the Chicken: Put the chicken in a bowl and stir 1/2 cup of the sauce mixture into it. Taste and season with additional salt if you think it needs it.
Soften the Corn Tortillas: Lay the tortillas out on a baking sheet (2 sheets if you have them, for more even heating), and lightly brush or spray both sides of the tortillas with oil. Bake just to warm through and soften, about 3 minutes. Stack the tortillas and cover with a towel to keep warm.
Build the Enchiladas: Smear about half of the sauce over the bottom of a 13x9-inch baking dish.
Working quickly so the tortillas stay hot and pliable, roll a portion of the chicken into each tortilla, (don't over-fill) then line them all up in the baking dishes. Douse evenly with the remaining sauce, then sprinkle with the cheese.
Bake until the enchiladas are hot through (the cheese will have begun to brown), about 15 minutes.
Garnish with onion rings, slices of jalapeno pepper and cilantro sprigs. These are best served piping hot from the oven.